LMFDB - Embedded newform 650.2.c.e.649.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(649,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.649"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-6,0,6,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.126157824.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 18x^{4} + 81x^{2} + 4 $ x^6 + 18x^4 + 81x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			649.1
Root			$-3.10548i$ of defining polynomial
Character	$\chi$	$=$	650.649
Dual form			650.2.c.e.649.6

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -3.10548i q^{3} +1.00000 q^{4} +3.10548i q^{6} +4.10548 q^{7} -1.00000 q^{8} -6.64402 q^{9} -1.53854i q^{11} -3.10548i q^{12} +(3.37475 - 1.26927i) q^{13} -4.10548 q^{14} +1.00000 q^{16} -3.00000i q^{17} +6.64402 q^{18} +1.10548i q^{19} -12.7495i q^{21} +1.53854i q^{22} -6.74950i q^{23} +3.10548i q^{24} +(-3.37475 + 1.26927i) q^{26} +11.3164i q^{27} +4.10548 q^{28} +5.56694 q^{29} +8.64402i q^{31} -1.00000 q^{32} -4.77791 q^{33} +3.00000i q^{34} -6.64402 q^{36} -4.53854 q^{37} -1.10548i q^{38} +(-3.94170 - 10.4802i) q^{39} -7.85499i q^{41} +12.7495i q^{42} +4.00000i q^{43} -1.53854i q^{44} +6.74950i q^{46} -10.8550 q^{47} -3.10548i q^{48} +9.85499 q^{49} -9.31645 q^{51} +(3.37475 - 1.26927i) q^{52} -0.433057i q^{53} -11.3164i q^{54} -4.10548 q^{56} +3.43306 q^{57} -5.56694 q^{58} +13.7779i q^{59} -14.3164 q^{61} -8.64402i q^{62} -27.2769 q^{63} +1.00000 q^{64} +4.77791 q^{66} -3.74950 q^{67} -3.00000i q^{68} -20.9605 q^{69} +6.64402 q^{72} +10.7779 q^{73} +4.53854 q^{74} +1.10548i q^{76} -6.31645i q^{77} +(3.94170 + 10.4802i) q^{78} +6.53854 q^{79} +15.2110 q^{81} +7.85499i q^{82} +4.46146 q^{83} -12.7495i q^{84} -4.00000i q^{86} -17.2880i q^{87} +1.53854i q^{88} +1.85499i q^{89} +(13.8550 - 5.21097i) q^{91} -6.74950i q^{92} +26.8439 q^{93} +10.8550 q^{94} +3.10548i q^{96} -3.78903 q^{97} -9.85499 q^{98} +10.2221i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} + 6 q^{7} - 6 q^{8} - 18 q^{9} - 6 q^{14} + 6 q^{16} + 18 q^{18} + 6 q^{28} + 18 q^{29} - 6 q^{32} + 24 q^{33} - 18 q^{36} - 24 q^{37} + 12 q^{39} - 6 q^{47} - 6 q^{56} + 36 q^{57}+ \cdots - 60 q^{97}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 + 6 * q^7 - 6 * q^8 - 18 * q^9 - 6 * q^14 + 6 * q^16 + 18 * q^18 + 6 * q^28 + 18 * q^29 - 6 * q^32 + 24 * q^33 - 18 * q^36 - 24 * q^37 + 12 * q^39 - 6 * q^47 - 6 * q^56 + 36 * q^57 - 18 * q^58 - 30 * q^61 - 30 * q^63 + 6 * q^64 - 24 * q^66 + 18 * q^67 - 48 * q^69 + 18 * q^72 + 12 * q^73 + 24 * q^74 - 12 * q^78 + 36 * q^79 + 54 * q^81 + 30 * q^83 + 24 * q^91 + 12 * q^93 + 6 * q^94 - 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	3.10548i		−	1.79295i	−0.443093	−	0.896476i	$-0.646119\pi$
$3$		−	3.10548i		−	1.79295i	0.443093	−	0.896476i	$-0.353881\pi$
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$			3.10548i			1.26781i
$7$	4.10548			1.55173			0.775863	−	0.630901i	$-0.217315\pi$
$7$	4.10548			1.55173			0.775863	+	0.630901i	$0.217315\pi$
$8$	−1.00000			−0.353553
$9$	−6.64402			−2.21467
$10$		0			0
$11$		−	1.53854i		−	0.463887i	−0.972729	−	0.231944i	$-0.925492\pi$
$11$		−	1.53854i		−	0.463887i	0.972729	−	0.231944i	$-0.0745085\pi$
$12$		−	3.10548i		−	0.896476i
$13$	3.37475	−	1.26927i	0.935988	−	0.352032i
$13$	3.37475	−	1.26927i	0.935988	−	0.352032i
$14$	−4.10548			−1.09724
$15$		0			0
$16$	1.00000			0.250000
$17$		−	3.00000i		−	0.727607i	−0.931476	−	0.363803i	$-0.881478\pi$
$17$		−	3.00000i		−	0.727607i	0.931476	−	0.363803i	$-0.118522\pi$
$18$	6.64402			1.56601
$19$			1.10548i			0.253615i	0.991927	+	0.126808i	$0.0404731\pi$
$19$			1.10548i			0.253615i	−0.991927	+	0.126808i	$0.959527\pi$
$20$		0			0
$21$		−	12.7495i		−	2.78217i
$22$			1.53854i			0.328018i
$23$		−	6.74950i		−	1.40737i	−0.710513	−	0.703685i	$-0.751537\pi$
$23$		−	6.74950i		−	1.40737i	0.710513	−	0.703685i	$-0.248463\pi$
$24$			3.10548i			0.633904i
$25$		0			0
$26$	−3.37475	+	1.26927i	−0.661843	+	0.248924i
$27$			11.3164i			2.17785i
$28$	4.10548			0.775863
$29$	5.56694			1.03376			0.516878	−	0.856059i	$-0.327094\pi$
$29$	5.56694			1.03376			0.516878	+	0.856059i	$0.327094\pi$
$30$		0			0
$31$			8.64402i			1.55251i	0.630418	+	0.776256i	$0.282884\pi$
$31$			8.64402i			1.55251i	−0.630418	+	0.776256i	$0.717116\pi$
$32$	−1.00000			−0.176777
$33$	−4.77791			−0.831727
$34$			3.00000i			0.514496i
$35$		0			0
$36$	−6.64402			−1.10734
$37$	−4.53854			−0.746131			−0.373066	−	0.927805i	$-0.621693\pi$
$37$	−4.53854			−0.746131			−0.373066	+	0.927805i	$0.621693\pi$
$38$		−	1.10548i		−	0.179333i
$39$	−3.94170	−	10.4802i	−0.631176	−	1.67818i
$40$		0			0
$41$		−	7.85499i		−	1.22674i	−0.789795	−	0.613371i	$-0.789813\pi$
$41$		−	7.85499i		−	1.22674i	0.789795	−	0.613371i	$-0.210187\pi$
$42$			12.7495i			1.96729i
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$		−	1.53854i		−	0.231944i
$45$		0			0
$46$			6.74950i			0.995160i
$47$	−10.8550			−1.58336			−0.791681	−	0.610934i	$-0.790794\pi$
$47$	−10.8550			−1.58336			−0.791681	+	0.610934i	$0.790794\pi$
$48$		−	3.10548i		−	0.448238i
$49$	9.85499			1.40786
$50$		0			0
$51$	−9.31645			−1.30456
$52$	3.37475	−	1.26927i	0.467994	−	0.176016i
$53$		−	0.433057i		−	0.0594850i	−0.999558	−	0.0297425i	$-0.990531\pi$
$53$		−	0.433057i		−	0.0594850i	0.999558	−	0.0297425i	$-0.00946872\pi$
$54$		−	11.3164i		−	1.53997i
$55$		0			0
$56$	−4.10548			−0.548618
$57$	3.43306			0.454720
$58$	−5.56694			−0.730975
$59$			13.7779i			1.79373i	0.442304	+	0.896865i	$0.354161\pi$
$59$			13.7779i			1.79373i	−0.442304	+	0.896865i	$0.645839\pi$
$60$		0			0
$61$	−14.3164			−1.83303			−0.916517	−	0.399997i	$-0.869011\pi$
$61$	−14.3164			−1.83303			−0.916517	+	0.399997i	$0.869011\pi$
$62$		−	8.64402i		−	1.09779i
$63$	−27.2769			−3.43657
$64$	1.00000			0.125000
$65$		0			0
$66$	4.77791			0.588120
$67$	−3.74950			−0.458075			−0.229037	−	0.973418i	$-0.573558\pi$
$67$	−3.74950			−0.458075			−0.229037	+	0.973418i	$0.573558\pi$
$68$		−	3.00000i		−	0.363803i
$69$	−20.9605			−2.52334
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	6.64402			0.783006
$73$	10.7779			1.26146			0.630729	−	0.776003i	$-0.282756\pi$
$73$	10.7779			1.26146			0.630729	+	0.776003i	$0.282756\pi$
$74$	4.53854			0.527595
$75$		0			0
$76$			1.10548i			0.126808i
$77$		−	6.31645i		−	0.719826i
$78$	3.94170	+	10.4802i	0.446309	+	1.18665i
$79$	6.53854			0.735643			0.367822	−	0.929896i	$-0.380104\pi$
$79$	6.53854			0.735643			0.367822	+	0.929896i	$0.380104\pi$
$80$		0			0
$81$	15.2110			1.69011
$82$			7.85499i			0.867438i
$83$	4.46146			0.489709			0.244854	−	0.969560i	$-0.421260\pi$
$83$	4.46146			0.489709			0.244854	+	0.969560i	$0.421260\pi$
$84$		−	12.7495i		−	1.39109i
$85$		0			0
$86$		−	4.00000i		−	0.431331i
$87$		−	17.2880i		−	1.85347i
$88$			1.53854i			0.164009i
$89$			1.85499i			0.196628i	0.995155	+	0.0983141i	$0.0313450\pi$
$89$			1.85499i			0.196628i	−0.995155	+	0.0983141i	$0.968655\pi$
$90$		0			0
$91$	13.8550	−	5.21097i	1.45240	−	0.546258i
$92$		−	6.74950i		−	0.703685i
$93$	26.8439			2.78358
$94$	10.8550			1.11961
$95$		0			0
$96$			3.10548i			0.316952i
$97$	−3.78903			−0.384718			−0.192359	−	0.981325i	$-0.561614\pi$
$97$	−3.78903			−0.384718			−0.192359	+	0.981325i	$0.561614\pi$
$98$	−9.85499			−0.995504
$99$			10.2221i			1.02736i
$100$		0			0
$101$	7.18256			0.714692			0.357346	−	0.933972i	$-0.383682\pi$
$101$	7.18256			0.714692			0.357346	+	0.933972i	$0.383682\pi$
$102$	9.31645			0.922466
$103$		−	12.5385i		−	1.23546i	−0.786391	−	0.617730i	$-0.788053\pi$
$103$		−	12.5385i		−	1.23546i	0.786391	−	0.617730i	$-0.211947\pi$
$104$	−3.37475	+	1.26927i	−0.330922	+	0.124462i
$105$		0			0
$106$			0.433057i			0.0420622i
$107$			1.81744i			0.175698i	0.996134	+	0.0878492i	$0.0279994\pi$
$107$			1.81744i			0.175698i	−0.996134	+	0.0878492i	$0.972001\pi$
$108$			11.3164i			1.08893i
$109$		−	3.67243i		−	0.351755i	−0.984412	−	0.175877i	$-0.943724\pi$
$109$		−	3.67243i		−	0.351755i	0.984412	−	0.175877i	$-0.0562762\pi$
$110$		0			0
$111$			14.0944i			1.33778i
$112$	4.10548			0.387932
$113$			16.0660i			1.51136i	0.654942	+	0.755679i	$0.272693\pi$
$113$			16.0660i			1.51136i	−0.654942	+	0.755679i	$0.727307\pi$
$114$	−3.43306			−0.321535
$115$		0			0
$116$	5.56694			0.516878
$117$	−22.4219	+	8.43306i	−2.07291	+	0.779636i
$118$		−	13.7779i		−	1.26836i
$119$		−	12.3164i		−	1.12905i
$120$		0			0
$121$	8.63290			0.784809
$122$	14.3164			1.29615
$123$	−24.3935			−2.19949
$124$			8.64402i			0.776256i
$125$		0			0
$126$	27.2769			2.43002
$127$		−	4.92292i		−	0.436839i	−0.975855	−	0.218419i	$-0.929910\pi$
$127$		−	4.92292i		−	0.436839i	0.975855	−	0.218419i	$-0.0700900\pi$
$128$	−1.00000			−0.0883883
$129$	12.4219			1.09369
$130$		0			0
$131$	0.866114			0.0756727			0.0378364	−	0.999284i	$-0.487953\pi$
$131$	0.866114			0.0756727			0.0378364	+	0.999284i	$0.487953\pi$
$132$	−4.77791			−0.415864
$133$			4.53854i			0.393541i
$134$	3.74950			0.323908
$135$		0			0
$136$			3.00000i			0.257248i
$137$	16.7779			1.43343			0.716717	−	0.697364i	$-0.245644\pi$
$137$	16.7779			1.43343			0.716717	+	0.697364i	$0.245644\pi$
$138$	20.9605			1.78427
$139$	4.39353			0.372654			0.186327	−	0.982488i	$-0.440342\pi$
$139$	4.39353			0.372654			0.186327	+	0.982488i	$0.440342\pi$
$140$		0			0
$141$			33.7100i			2.83889i
$142$		0			0
$143$	−1.95282	−	5.19219i	−0.163303	−	0.434193i
$144$	−6.64402			−0.553669
$145$		0			0
$146$	−10.7779			−0.891986
$147$		−	30.6045i		−	2.52422i
$148$	−4.53854			−0.373066
$149$			9.70998i			0.795472i	0.917500	+	0.397736i	$0.130204\pi$
$149$			9.70998i			0.795472i	−0.917500	+	0.397736i	$0.869796\pi$
$150$		0			0
$151$		−	2.48986i		−	0.202622i	−0.994855	−	0.101311i	$-0.967696\pi$
$151$		−	2.48986i		−	0.202622i	0.994855	−	0.101311i	$-0.0323038\pi$
$152$		−	1.10548i		−	0.0896665i
$153$			19.9321i			1.61141i
$154$			6.31645i			0.508994i
$155$		0			0
$156$	−3.94170	−	10.4802i	−0.315588	−	0.839090i
$157$			11.3935i			0.909302i	0.890670	+	0.454651i	$0.150236\pi$
$157$			11.3935i			0.909302i	−0.890670	+	0.454651i	$0.849764\pi$
$158$	−6.53854			−0.520178
$159$	−1.34485			−0.106654
$160$		0			0
$161$		−	27.7100i		−	2.18385i
$162$	−15.2110			−1.19509
$163$	−16.8155			−1.31709			−0.658544	−	0.752542i	$-0.728827\pi$
$163$	−16.8155			−1.31709			−0.658544	+	0.752542i	$0.728827\pi$
$164$		−	7.85499i		−	0.613371i
$165$		0			0
$166$	−4.46146			−0.346276
$167$	1.61562			0.125020			0.0625102	−	0.998044i	$-0.480089\pi$
$167$	1.61562			0.125020			0.0625102	+	0.998044i	$0.480089\pi$
$168$			12.7495i			0.983646i
$169$	9.77791	−	8.56694i	0.752147	−	0.658996i
$170$		0			0
$171$		−	7.34485i		−	0.561675i
$172$			4.00000i			0.304997i
$173$		−	12.3164i		−	0.936402i	−0.883622	−	0.468201i	$-0.844902\pi$
$173$		−	12.3164i		−	0.936402i	0.883622	−	0.468201i	$-0.155098\pi$
$174$			17.2880i			1.31060i
$175$		0			0
$176$		−	1.53854i		−	0.115972i
$177$	42.7871			3.21607
$178$		−	1.85499i		−	0.139037i
$179$	−10.1826			−0.761080			−0.380540	−	0.924764i	$-0.624262\pi$
$179$	−10.1826			−0.761080			−0.380540	+	0.924764i	$0.624262\pi$
$180$		0			0
$181$	11.3935			0.846874			0.423437	−	0.905926i	$-0.360823\pi$
$181$	11.3935			0.846874			0.423437	+	0.905926i	$0.360823\pi$
$182$	−13.8550	+	5.21097i	−1.02700	+	0.386262i
$183$			44.4595i			3.28654i
$184$			6.74950i			0.497580i
$185$		0			0
$186$	−26.8439			−1.96829
$187$	−4.61562			−0.337527
$188$	−10.8550			−0.791681
$189$			46.4595i			3.37943i
$190$		0			0
$191$	−19.4990			−1.41090			−0.705449	−	0.708760i	$-0.749255\pi$
$191$	−19.4990			−1.41090			−0.705449	+	0.708760i	$0.749255\pi$
$192$		−	3.10548i		−	0.224119i
$193$	2.72110			0.195869			0.0979346	−	0.995193i	$-0.468776\pi$
$193$	2.72110			0.195869			0.0979346	+	0.995193i	$0.468776\pi$
$194$	3.78903			0.272037
$195$		0			0
$196$	9.85499			0.703928
$197$	1.61562			0.115108			0.0575540	−	0.998342i	$-0.481670\pi$
$197$	1.61562			0.115108			0.0575540	+	0.998342i	$0.481670\pi$
$198$		−	10.2221i		−	0.726452i
$199$	22.2485			1.57716			0.788578	−	0.614935i	$-0.210818\pi$
$199$	22.2485			1.57716			0.788578	+	0.614935i	$0.210818\pi$
$200$		0			0
$201$			11.6440i			0.821306i
$202$	−7.18256			−0.505363
$203$	22.8550			1.60411
$204$	−9.31645			−0.652282
$205$		0			0
$206$			12.5385i			0.873601i
$207$			44.8439i			3.11686i
$208$	3.37475	−	1.26927i	0.233997	−	0.0880080i
$209$	1.70083			0.117649
$210$		0			0
$211$	10.2394			0.704907			0.352454	−	0.935829i	$-0.385347\pi$
$211$	10.2394			0.704907			0.352454	+	0.935829i	$0.385347\pi$
$212$		−	0.433057i		−	0.0297425i
$213$		0			0
$214$		−	1.81744i		−	0.124238i
$215$		0			0
$216$		−	11.3164i		−	0.769987i
$217$			35.4879i			2.40907i
$218$			3.67243i			0.248728i
$219$		−	33.4706i		−	2.26173i
$220$		0			0
$221$	−3.80781	−	10.1243i	−0.256141	−	0.681031i
$222$		−	14.0944i		−	0.945951i
$223$	20.9605			1.40362			0.701808	−	0.712366i	$-0.252376\pi$
$223$	20.9605			1.40362			0.701808	+	0.712366i	$0.252376\pi$
$224$	−4.10548			−0.274309
$225$		0			0
$226$		−	16.0660i		−	1.06869i
$227$	4.85499			0.322237			0.161118	−	0.986935i	$-0.448490\pi$
$227$	4.85499			0.322237			0.161118	+	0.986935i	$0.448490\pi$
$228$	3.43306			0.227360
$229$			6.71196i			0.443538i	0.975099	+	0.221769i	$0.0711832\pi$
$229$			6.71196i			0.443538i	−0.975099	+	0.221769i	$0.928817\pi$
$230$		0			0
$231$	−19.6156			−1.29061
$232$	−5.56694			−0.365488
$233$			14.3651i			0.941091i	0.882376	+	0.470545i	$0.155943\pi$
$233$			14.3651i			0.941091i	−0.882376	+	0.470545i	$0.844057\pi$
$234$	22.4219	−	8.43306i	1.46577	−	0.551286i
$235$		0			0
$236$			13.7779i			0.896865i
$237$		−	20.3053i		−	1.31897i
$238$			12.3164i			0.798357i
$239$			1.14501i			0.0740647i	0.999314	+	0.0370324i	$0.0117905\pi$
$239$			1.14501i			0.0740647i	−0.999314	+	0.0370324i	$0.988210\pi$
$240$		0			0
$241$		−	20.5669i		−	1.32483i	−0.749136	−	0.662417i	$-0.769531\pi$
$241$		−	20.5669i		−	1.32483i	0.749136	−	0.662417i	$-0.230469\pi$
$242$	−8.63290			−0.554944
$243$		−	13.2880i		−	0.852428i
$244$	−14.3164			−0.916517
$245$		0			0
$246$	24.3935			1.55527
$247$	1.40316	+	3.73073i	0.0892807	+	0.237381i
$248$		−	8.64402i		−	0.548896i
$249$		−	13.8550i		−	0.878024i
$250$		0			0
$251$	3.31645			0.209332			0.104666	−	0.994507i	$-0.466623\pi$
$251$	3.31645			0.209332			0.104666	+	0.994507i	$0.466623\pi$
$252$	−27.2769			−1.71828
$253$	−10.3844			−0.652860
$254$			4.92292i			0.308892i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	12.4331i		−	0.775553i	−0.921753	−	0.387776i	$-0.873243\pi$
$257$		−	12.4331i		−	0.775553i	0.921753	−	0.387776i	$-0.126757\pi$
$258$	−12.4219			−0.773356
$259$	−18.6329			−1.15779
$260$		0			0
$261$	−36.9869			−2.28943
$262$	−0.866114			−0.0535087
$263$			4.38438i			0.270353i	0.990822	+	0.135176i	$0.0431601\pi$
$263$			4.38438i			0.270353i	−0.990822	+	0.135176i	$0.956840\pi$
$264$	4.77791			0.294060
$265$		0			0
$266$		−	4.53854i		−	0.278276i
$267$	5.76063			0.352545
$268$	−3.74950			−0.229037
$269$	5.56694			0.339423			0.169711	−	0.985494i	$-0.445716\pi$
$269$	5.56694			0.339423			0.169711	+	0.985494i	$0.445716\pi$
$270$		0			0
$271$			9.39353i			0.570616i	0.958436	+	0.285308i	$0.0920959\pi$
$271$			9.39353i			0.570616i	−0.958436	+	0.285308i	$0.907904\pi$
$272$		−	3.00000i		−	0.181902i
$273$	−16.1826	−	43.0264i	−0.979413	−	2.60408i
$274$	−16.7779			−1.01359
$275$		0			0
$276$	−20.9605			−1.26167
$277$		−	8.38438i		−	0.503769i	−0.967757	−	0.251884i	$-0.918950\pi$
$277$		−	8.38438i		−	0.503769i	0.967757	−	0.251884i	$-0.0810502\pi$
$278$	−4.39353			−0.263506
$279$		−	57.4311i		−	3.43831i
$280$		0			0
$281$			12.6329i			0.753615i	0.926292	+	0.376808i	$0.122978\pi$
$281$			12.6329i			0.753615i	−0.926292	+	0.376808i	$0.877022\pi$
$282$		−	33.7100i		−	2.00740i
$283$		−	13.4706i		−	0.800744i	−0.916353	−	0.400372i	$-0.868881\pi$
$283$		−	13.4706i		−	0.800744i	0.916353	−	0.400372i	$-0.131119\pi$
$284$		0			0
$285$		0			0
$286$	1.95282	+	5.19219i	0.115473	+	0.307021i
$287$		−	32.2485i		−	1.90357i
$288$	6.64402			0.391503
$289$	8.00000			0.470588
$290$		0			0
$291$			11.7668i			0.689781i
$292$	10.7779			0.630729
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$			30.6045i			1.78489i
$295$		0			0
$296$	4.53854			0.263797
$297$	17.4108			1.01028
$298$		−	9.70998i		−	0.562484i
$299$	−8.56694	−	22.7779i	−0.495439	−	1.31728i
$300$		0			0
$301$			16.4219i			0.946544i
$302$			2.48986i			0.143276i
$303$		−	22.3053i		−	1.28141i
$304$			1.10548i			0.0634038i
$305$		0			0
$306$		−	19.9321i		−	1.13944i
$307$	−13.8925			−0.792889			−0.396444	−	0.918059i	$-0.629756\pi$
$307$	−13.8925			−0.792889			−0.396444	+	0.918059i	$0.629756\pi$
$308$		−	6.31645i		−	0.359913i
$309$	−38.9382			−2.21512
$310$		0			0
$311$	3.51827			0.199503			0.0997513	−	0.995012i	$-0.468195\pi$
$311$	3.51827			0.199503			0.0997513	+	0.995012i	$0.468195\pi$
$312$	3.94170	+	10.4802i	0.223155	+	0.593326i
$313$		−	24.5650i		−	1.38849i	−0.719737	−	0.694247i	$-0.755738\pi$
$313$		−	24.5650i		−	1.38849i	0.719737	−	0.694247i	$-0.244262\pi$
$314$		−	11.3935i		−	0.642974i
$315$		0			0
$316$	6.53854			0.367822
$317$	−1.46146			−0.0820838			−0.0410419	−	0.999157i	$-0.513068\pi$
$317$	−1.46146			−0.0820838			−0.0410419	+	0.999157i	$0.513068\pi$
$318$	1.34485			0.0754155
$319$		−	8.56496i		−	0.479546i
$320$		0			0
$321$	5.64402			0.315019
$322$			27.7100i			1.54422i
$323$	3.31645			0.184532
$324$	15.2110			0.845054
$325$		0			0
$326$	16.8155			0.931322
$327$	−11.4047			−0.630679
$328$			7.85499i			0.433719i
$329$	−44.5650			−2.45695
$330$		0			0
$331$			18.2394i			1.00253i	0.865295	+	0.501263i	$0.167131\pi$
$331$			18.2394i			1.00253i	−0.865295	+	0.501263i	$0.832869\pi$
$332$	4.46146			0.244854
$333$	30.1542			1.65244
$334$	−1.61562			−0.0884027
$335$		0			0
$336$		−	12.7495i		−	0.695543i
$337$			19.6329i			1.06947i	0.845019	+	0.534736i	$0.179589\pi$
$337$			19.6329i			1.06947i	−0.845019	+	0.534736i	$0.820411\pi$
$338$	−9.77791	+	8.56694i	−0.531848	+	0.465980i
$339$	49.8925			2.70979
$340$		0			0
$341$	13.2992			0.720190
$342$			7.34485i			0.397164i
$343$	11.7211			0.632880
$344$		−	4.00000i		−	0.215666i
$345$		0			0
$346$			12.3164i			0.662136i
$347$			23.6816i			1.27129i	0.771980	+	0.635647i	$0.219266\pi$
$347$			23.6816i			1.27129i	−0.771980	+	0.635647i	$0.780734\pi$
$348$		−	17.2880i		−	0.926736i
$349$			0.154159i			0.00825192i	0.999991	+	0.00412596i	$0.00131334\pi$
$349$			0.154159i			0.00825192i	−0.999991	+	0.00412596i	$0.998687\pi$
$350$		0			0
$351$	14.3636	+	38.1902i	0.766674	+	2.03844i
$352$			1.53854i			0.0820044i
$353$	−36.6329			−1.94977			−0.974886	−	0.222704i	$-0.928512\pi$
$353$	−36.6329			−1.94977			−0.974886	+	0.222704i	$0.928512\pi$
$354$	−42.7871			−2.27411
$355$		0			0
$356$			1.85499i			0.0983141i
$357$	−38.2485			−2.02433
$358$	10.1826			0.538165
$359$			27.2394i			1.43764i	0.695197	+	0.718819i	$0.255317\pi$
$359$			27.2394i			1.43764i	−0.695197	+	0.718819i	$0.744683\pi$
$360$		0			0
$361$	17.7779			0.935679
$362$	−11.3935			−0.598830
$363$		−	26.8093i		−	1.40712i
$364$	13.8550	−	5.21097i	0.726199	−	0.273129i
$365$		0			0
$366$		−	44.4595i		−	2.32393i
$367$			23.8641i			1.24570i	0.782342	+	0.622849i	$0.214025\pi$
$367$			23.8641i			1.24570i	−0.782342	+	0.622849i	$0.785975\pi$
$368$		−	6.74950i		−	0.351842i
$369$			52.1887i			2.71684i
$370$		0			0
$371$		−	1.77791i		−	0.0923044i
$372$	26.8439			1.39179
$373$		−	22.3164i		−	1.15550i	−0.816213	−	0.577751i	$-0.803930\pi$
$373$		−	22.3164i		−	1.15550i	0.816213	−	0.577751i	$-0.196070\pi$
$374$	4.61562			0.238668
$375$		0			0
$376$	10.8550			0.559803
$377$	18.7871	−	7.06595i	0.967583	−	0.363915i
$378$		−	46.4595i		−	2.38962i
$379$			9.74950i			0.500798i	0.968143	+	0.250399i	$0.0805619\pi$
$379$			9.74950i			0.500798i	−0.968143	+	0.250399i	$0.919438\pi$
$380$		0			0
$381$	−15.2880			−0.783230
$382$	19.4990			0.997656
$383$	24.7871			1.26656			0.633280	−	0.773923i	$-0.281708\pi$
$383$	24.7871			1.26656			0.633280	+	0.773923i	$0.281708\pi$
$384$			3.10548i			0.158476i
$385$		0			0
$386$	−2.72110			−0.138500
$387$		−	26.5761i		−	1.35094i
$388$	−3.78903			−0.192359
$389$	0.749505			0.0380014			0.0190007	−	0.999819i	$-0.493952\pi$
$389$	0.749505			0.0380014			0.0190007	+	0.999819i	$0.493952\pi$
$390$		0			0
$391$	−20.2485			−1.02401
$392$	−9.85499			−0.497752
$393$		−	2.68970i		−	0.135678i
$394$	−1.61562			−0.0813937
$395$		0			0
$396$			10.2221i			0.513679i
$397$	9.67243			0.485445			0.242723	−	0.970096i	$-0.421960\pi$
$397$	9.67243			0.485445			0.242723	+	0.970096i	$0.421960\pi$
$398$	−22.2485			−1.11522
$399$	14.0944			0.705600
$400$		0			0
$401$		−	10.9321i		−	0.545921i	−0.962025	−	0.272961i	$-0.911997\pi$
$401$		−	10.9321i		−	0.545921i	0.962025	−	0.272961i	$-0.0880029\pi$
$402$		−	11.6440i		−	0.580751i
$403$	10.9716	+	29.1714i	0.546534	+	1.45313i
$404$	7.18256			0.357346
$405$		0			0
$406$	−22.8550			−1.13427
$407$			6.98272i			0.346121i
$408$	9.31645			0.461233
$409$		−	26.5669i		−	1.31365i	−0.754043	−	0.656825i	$-0.771899\pi$
$409$		−	26.5669i		−	1.31365i	0.754043	−	0.656825i	$-0.228101\pi$
$410$		0			0
$411$		−	52.1035i		−	2.57008i
$412$		−	12.5385i		−	0.617730i
$413$			56.5650i			2.78338i
$414$		−	44.8439i		−	2.20396i
$415$		0			0
$416$	−3.37475	+	1.26927i	−0.165461	+	0.0622311i
$417$		−	13.6440i		−	0.668151i
$418$	−1.70083			−0.0831903
$419$	−24.3145			−1.18784			−0.593920	−	0.804524i	$-0.702420\pi$
$419$	−24.3145			−1.18784			−0.593920	+	0.804524i	$0.702420\pi$
$420$		0			0
$421$			6.15416i			0.299935i	0.988691	+	0.149968i	$0.0479170\pi$
$421$			6.15416i			0.299935i	−0.988691	+	0.149968i	$0.952083\pi$
$422$	−10.2394			−0.498445
$423$	72.1208			3.50663
$424$			0.433057i			0.0210311i
$425$		0			0
$426$		0			0
$427$	−58.7759			−2.84437
$428$			1.81744i			0.0878492i
$429$	−16.1243	+	6.06445i	−0.778486	+	0.292795i
$430$		0			0
$431$		−	0.828565i		−	0.0399106i	−0.999801	−	0.0199553i	$-0.993648\pi$
$431$		−	0.828565i		−	0.0399106i	0.999801	−	0.0199553i	$-0.00635238\pi$
$432$			11.3164i			0.544463i
$433$			15.7008i			0.754534i	0.926105	+	0.377267i	$0.123136\pi$
$433$			15.7008i			0.754534i	−0.926105	+	0.377267i	$0.876864\pi$
$434$		−	35.4879i		−	1.70347i
$435$		0			0
$436$		−	3.67243i		−	0.175877i
$437$	7.46146			0.356930
$438$			33.4706i			1.59929i
$439$	9.17144			0.437729			0.218864	−	0.975755i	$-0.429765\pi$
$439$	9.17144			0.437729			0.218864	+	0.975755i	$0.429765\pi$
$440$		0			0
$441$	−65.4768			−3.11794
$442$	3.80781	+	10.1243i	0.181119	+	0.481562i
$443$			15.3164i			0.727706i	0.931456	+	0.363853i	$0.118539\pi$
$443$			15.3164i			0.727706i	−0.931456	+	0.363853i	$0.881461\pi$
$444$			14.0944i			0.668889i
$445$		0			0
$446$	−20.9605			−0.992507
$447$	30.1542			1.42624
$448$	4.10548			0.193966
$449$		−	23.4108i		−	1.10482i	−0.833571	−	0.552412i	$-0.813708\pi$
$449$		−	23.4108i		−	1.10482i	0.833571	−	0.552412i	$-0.186292\pi$
$450$		0			0
$451$	−12.0852			−0.569070
$452$			16.0660i			0.755679i
$453$	−7.73223			−0.363292
$454$	−4.85499			−0.227856
$455$		0			0
$456$	−3.43306			−0.160768
$457$	22.9321			1.07272			0.536358	−	0.843990i	$-0.319800\pi$
$457$	22.9321			1.07272			0.536358	+	0.843990i	$0.319800\pi$
$458$		−	6.71196i		−	0.313629i
$459$	33.9493			1.58462
$460$		0			0
$461$			13.4615i			0.626963i	0.949594	+	0.313481i	$0.101495\pi$
$461$			13.4615i			0.626963i	−0.949594	+	0.313481i	$0.898505\pi$
$462$	19.6156			0.912601
$463$	−16.0264			−0.744811			−0.372406	−	0.928070i	$-0.621467\pi$
$463$	−16.0264			−0.744811			−0.372406	+	0.928070i	$0.621467\pi$
$464$	5.56694			0.258439
$465$		0			0
$466$		−	14.3651i		−	0.665452i
$467$			0.866114i			0.0400790i	0.999799	+	0.0200395i	$0.00637919\pi$
$467$			0.866114i			0.0400790i	−0.999799	+	0.0200395i	$0.993621\pi$
$468$	−22.4219	+	8.43306i	−1.03645	+	0.389818i
$469$	−15.3935			−0.710807
$470$		0			0
$471$	35.3824			1.63033
$472$		−	13.7779i		−	0.634180i
$473$	6.15416			0.282969
$474$			20.3053i			0.932654i
$475$		0			0
$476$		−	12.3164i		−	0.564523i
$477$			2.87724i			0.131740i
$478$		−	1.14501i		−	0.0523717i
$479$			29.4879i			1.34734i	0.739034	+	0.673668i	$0.235282\pi$
$479$			29.4879i			1.34734i	−0.739034	+	0.673668i	$0.764718\pi$
$480$		0			0
$481$	−15.3164	+	5.76063i	−0.698370	+	0.262662i
$482$			20.5669i			0.936799i
$483$	−86.0528			−3.91554
$484$	8.63290			0.392404
$485$		0			0
$486$			13.2880i			0.602758i
$487$	−35.4503			−1.60641			−0.803204	−	0.595704i	$-0.796873\pi$
$487$	−35.4503			−1.60641			−0.803204	+	0.595704i	$0.796873\pi$
$488$	14.3164			0.648075
$489$			52.2201i			2.36148i
$490$		0			0
$491$	−32.1319			−1.45009			−0.725046	−	0.688700i	$-0.758182\pi$
$491$	−32.1319			−1.45009			−0.725046	+	0.688700i	$0.758182\pi$
$492$	−24.3935			−1.09975
$493$		−	16.7008i		−	0.752168i
$494$	−1.40316	−	3.73073i	−0.0631310	−	0.167853i
$495$		0			0
$496$			8.64402i			0.388128i
$497$		0			0
$498$			13.8550i			0.620857i
$499$		−	27.2769i		−	1.22108i	−0.791984	−	0.610541i	$-0.790952\pi$
$499$		−	27.2769i		−	1.22108i	0.791984	−	0.610541i	$-0.209048\pi$
$500$		0			0
$501$		−	5.01728i		−	0.224155i
$502$	−3.31645			−0.148020
$503$			26.9980i			1.20378i	0.798578	+	0.601891i	$0.205586\pi$
$503$			26.9980i			1.20378i	−0.798578	+	0.601891i	$0.794414\pi$
$504$	27.2769			1.21501
$505$		0			0
$506$	10.3844			0.461642
$507$	−26.6045	−	30.3651i	−1.18155	−	1.34856i
$508$		−	4.92292i		−	0.218419i
$509$			38.8814i			1.72339i	0.507428	+	0.861694i	$0.330596\pi$
$509$			38.8814i			1.72339i	−0.507428	+	0.861694i	$0.669404\pi$
$510$		0			0
$511$	44.2485			1.95744
$512$	−1.00000			−0.0441942
$513$	−12.5101			−0.552336
$514$			12.4331i			0.548399i
$515$		0			0
$516$	12.4219			0.546845
$517$			16.7008i			0.734502i
$518$	18.6329			0.818682
$519$	−38.2485			−1.67892
$520$		0			0
$521$	4.06595			0.178133			0.0890663	−	0.996026i	$-0.471612\pi$
$521$	4.06595			0.178133			0.0890663	+	0.996026i	$0.471612\pi$
$522$	36.9869			1.61887
$523$			34.8723i			1.52486i	0.647072	+	0.762429i	$0.275993\pi$
$523$			34.8723i			1.52486i	−0.647072	+	0.762429i	$0.724007\pi$
$524$	0.866114			0.0378364
$525$		0			0
$526$		−	4.38438i		−	0.191168i
$527$	25.9321			1.12962
$528$	−4.77791			−0.207932
$529$	−22.5558			−0.980688
$530$		0			0
$531$		−	91.5407i		−	3.97253i
$532$			4.53854i			0.196771i
$533$	−9.97010	−	26.5086i	−0.431853	−	1.14822i
$534$	−5.76063			−0.249287
$535$		0			0
$536$	3.74950			0.161954
$537$			31.6218i			1.36458i
$538$	−5.56694			−0.240008
$539$		−	15.1623i		−	0.653086i
$540$		0			0
$541$			37.2282i			1.60057i	0.599622	+	0.800284i	$0.295318\pi$
$541$			37.2282i			1.60057i	−0.599622	+	0.800284i	$0.704682\pi$
$542$		−	9.39353i		−	0.403487i
$543$		−	35.3824i		−	1.51840i
$544$			3.00000i			0.128624i
$545$		0			0
$546$	16.1826	+	43.0264i	0.692550	+	1.84136i
$547$			35.9493i			1.53708i	0.639800	+	0.768541i	$0.279017\pi$
$547$			35.9493i			1.53708i	−0.639800	+	0.768541i	$0.720983\pi$
$548$	16.7779			0.716717
$549$	95.1188			4.05957
$550$		0			0
$551$			6.15416i			0.262176i
$552$	20.9605			0.892137
$553$	26.8439			1.14152
$554$			8.38438i			0.356218i
$555$		0			0
$556$	4.39353			0.186327
$557$	−14.0944			−0.597197			−0.298599	−	0.954379i	$-0.596519\pi$
$557$	−14.0944			−0.597197			−0.298599	+	0.954379i	$0.596519\pi$
$558$			57.4311i			2.43125i
$559$	5.07708	+	13.4990i	0.214738	+	0.570947i
$560$		0			0
$561$			14.3337i			0.605170i
$562$		−	12.6329i		−	0.532887i
$563$		−	28.2678i		−	1.19134i	−0.803228	−	0.595672i	$-0.796886\pi$
$563$		−	28.2678i		−	1.19134i	0.803228	−	0.595672i	$-0.203114\pi$
$564$			33.7100i			1.41945i
$565$		0			0
$566$			13.4706i			0.566212i
$567$	62.4484			2.62258
$568$		0			0
$569$	26.1339			1.09559			0.547795	−	0.836613i	$-0.315467\pi$
$569$	26.1339			1.09559			0.547795	+	0.836613i	$0.315467\pi$
$570$		0			0
$571$	10.7871			0.451424			0.225712	−	0.974194i	$-0.427529\pi$
$571$	10.7871			0.451424			0.225712	+	0.974194i	$0.427529\pi$
$572$	−1.95282	−	5.19219i	−0.0816516	−	0.217096i
$573$			60.5538i			2.52967i
$574$			32.2485i			1.34603i
$575$		0			0
$576$	−6.64402			−0.276834
$577$	12.1228			0.504677			0.252339	−	0.967639i	$-0.418800\pi$
$577$	12.1228			0.504677			0.252339	+	0.967639i	$0.418800\pi$
$578$	−8.00000			−0.332756
$579$		−	8.45033i		−	0.351184i
$580$		0			0
$581$	18.3164			0.759894
$582$		−	11.7668i		−	0.487749i
$583$	−0.666275			−0.0275943
$584$	−10.7779			−0.445993
$585$		0			0
$586$	−6.00000			−0.247858
$587$	−35.2485			−1.45486			−0.727431	−	0.686181i	$-0.759286\pi$
$587$	−35.2485			−1.45486			−0.727431	+	0.686181i	$0.759286\pi$
$588$		−	30.6045i		−	1.26211i
$589$	−9.55582			−0.393741
$590$		0			0
$591$		−	5.01728i		−	0.206383i
$592$	−4.53854			−0.186533
$593$	−11.0862			−0.455257			−0.227628	−	0.973748i	$-0.573097\pi$
$593$	−11.0862			−0.455257			−0.227628	+	0.973748i	$0.573097\pi$
$594$	−17.4108			−0.714374
$595$		0			0
$596$			9.70998i			0.397736i
$597$		−	69.0924i		−	2.82776i
$598$	8.56694	+	22.7779i	0.350328	+	0.931458i
$599$	−31.4990			−1.28701			−0.643507	−	0.765440i	$-0.722521\pi$
$599$	−31.4990			−1.28701			−0.643507	+	0.765440i	$0.722521\pi$
$600$		0			0
$601$	19.6329			0.800843			0.400421	−	0.916331i	$-0.368864\pi$
$601$	19.6329			0.800843			0.400421	+	0.916331i	$0.368864\pi$
$602$		−	16.4219i		−	0.669308i
$603$	24.9118			1.01449
$604$		−	2.48986i		−	0.101311i
$605$		0			0
$606$			22.3053i			0.906092i
$607$		−	17.6156i		−	0.714996i	−0.933914	−	0.357498i	$-0.883630\pi$
$607$		−	17.6156i		−	0.714996i	0.933914	−	0.357498i	$-0.116370\pi$
$608$		−	1.10548i		−	0.0448332i
$609$		−	70.9758i		−	2.87608i
$610$		0			0
$611$	−36.6329	+	13.7779i	−1.48201	+	0.557395i
$612$			19.9321i			0.805706i
$613$	−25.4200			−1.02670			−0.513351	−	0.858179i	$-0.671596\pi$
$613$	−25.4200			−1.02670			−0.513351	+	0.858179i	$0.671596\pi$
$614$	13.8925			0.560657
$615$		0			0
$616$			6.31645i			0.254497i
$617$	27.7100			1.11556			0.557781	−	0.829988i	$-0.311653\pi$
$617$	27.7100			1.11556			0.557781	+	0.829988i	$0.311653\pi$
$618$	38.9382			1.56632
$619$			20.8439i			0.837786i	0.908036	+	0.418893i	$0.137582\pi$
$619$			20.8439i			0.837786i	−0.908036	+	0.418893i	$0.862418\pi$
$620$		0			0
$621$	76.3804			3.06504
$622$	−3.51827			−0.141070
$623$			7.61562i			0.305113i
$624$	−3.94170	−	10.4802i	−0.157794	−	0.419545i
$625$		0			0
$626$			24.5650i			0.981813i
$627$		−	5.28189i		−	0.210939i
$628$			11.3935i			0.454651i
$629$			13.6156i			0.542890i
$630$		0			0
$631$		−	30.7495i		−	1.22412i	−0.790812	−	0.612059i	$-0.790341\pi$
$631$		−	30.7495i		−	1.22412i	0.790812	−	0.612059i	$-0.209659\pi$
$632$	−6.53854			−0.260089
$633$		−	31.7982i		−	1.26386i
$634$	1.46146			0.0580420
$635$		0			0
$636$	−1.34485			−0.0533268
$637$	33.2581	−	12.5086i	1.31774	−	0.495610i
$638$			8.56496i			0.339090i
$639$		0			0
$640$		0			0
$641$	19.0660			0.753060			0.376530	−	0.926404i	$-0.377117\pi$
$641$	19.0660			0.753060			0.376530	+	0.926404i	$0.377117\pi$
$642$	−5.64402			−0.222752
$643$	−45.8641			−1.80870			−0.904352	−	0.426786i	$-0.859646\pi$
$643$	−45.8641			−1.80870			−0.904352	+	0.426786i	$0.859646\pi$
$644$		−	27.7100i		−	1.09193i
$645$		0			0
$646$	−3.31645			−0.130484
$647$		−	11.0173i		−	0.433134i	−0.976268	−	0.216567i	$-0.930514\pi$
$647$		−	11.0173i		−	0.433134i	0.976268	−	0.216567i	$-0.0694860\pi$
$648$	−15.2110			−0.597543
$649$	21.1979			0.832089
$650$		0			0
$651$	110.207			4.31935
$652$	−16.8155			−0.658544
$653$		−	14.5650i		−	0.569971i	−0.958532	−	0.284986i	$-0.908011\pi$
$653$		−	14.5650i		−	0.569971i	0.958532	−	0.284986i	$-0.0919888\pi$
$654$	11.4047			0.445957
$655$		0			0
$656$		−	7.85499i		−	0.306686i
$657$	−71.6087			−2.79372
$658$	44.5650			1.73732
$659$	−19.8174			−0.771978			−0.385989	−	0.922503i	$-0.626140\pi$
$659$	−19.8174			−0.771978			−0.385989	+	0.922503i	$0.626140\pi$
$660$		0			0
$661$		−	13.4615i		−	0.523590i	−0.965123	−	0.261795i	$-0.915686\pi$
$661$		−	13.4615i		−	0.523590i	0.965123	−	0.261795i	$-0.0843145\pi$
$662$		−	18.2394i		−	0.708893i
$663$	−31.4407	+	11.8251i	−1.22106	+	0.459248i
$664$	−4.46146			−0.173138
$665$		0			0
$666$	−30.1542			−1.16845
$667$		−	37.5741i		−	1.45488i
$668$	1.61562			0.0625102
$669$		−	65.0924i		−	2.51662i
$670$		0			0
$671$			22.0264i			0.850321i
$672$			12.7495i			0.491823i
$673$		−	0.0679332i		−	0.00261863i	−0.999999	−	0.00130932i	$-0.999583\pi$
$673$		−	0.0679332i		−	0.00261863i	0.999999	−	0.00130932i	$-0.000416768\pi$
$674$		−	19.6329i		−	0.756231i
$675$		0			0
$676$	9.77791	−	8.56694i	0.376073	−	0.329498i
$677$			26.1319i			1.00433i	0.864772	+	0.502165i	$0.167463\pi$
$677$			26.1319i			1.00433i	−0.864772	+	0.502165i	$0.832537\pi$
$678$	−49.8925			−1.91611
$679$	−15.5558			−0.596977
$680$		0			0
$681$		−	15.0771i		−	0.577755i
$682$	−13.2992			−0.509252
$683$	17.0944			0.654097			0.327049	−	0.945007i	$-0.393946\pi$
$683$	17.0944			0.654097			0.327049	+	0.945007i	$0.393946\pi$
$684$		−	7.34485i		−	0.280837i
$685$		0			0
$686$	−11.7211			−0.447514
$687$	20.8439			0.795243
$688$			4.00000i			0.152499i
$689$	−0.549666	−	1.46146i	−0.0209406	−	0.0556772i
$690$		0			0
$691$			25.3844i			0.965667i	0.875712	+	0.482834i	$0.160392\pi$
$691$			25.3844i			0.965667i	−0.875712	+	0.482834i	$0.839608\pi$
$692$		−	12.3164i		−	0.468201i
$693$			41.9666i			1.59418i
$694$		−	23.6816i		−	0.898940i
$695$		0			0
$696$			17.2880i			0.655302i
$697$	−23.5650			−0.892587
$698$		−	0.154159i		−	0.00583499i
$699$	44.6106			1.68733
$700$		0			0
$701$	9.43108			0.356207			0.178103	−	0.984012i	$-0.443004\pi$
$701$	9.43108			0.356207			0.178103	+	0.984012i	$0.443004\pi$
$702$	−14.3636	−	38.1902i	−0.542120	−	1.44140i
$703$		−	5.01728i		−	0.189230i
$704$		−	1.53854i		−	0.0579859i
$705$		0			0
$706$	36.6329			1.37870
$707$	29.4879			1.10901
$708$	42.7871			1.60804
$709$			20.1734i			0.757629i	0.925473	+	0.378814i	$0.123668\pi$
$709$			20.1734i			0.757629i	−0.925473	+	0.378814i	$0.876332\pi$
$710$		0			0
$711$	−43.4422			−1.62921
$712$		−	1.85499i		−	0.0695186i
$713$	58.3429			2.18496
$714$	38.2485			1.43141
$715$		0			0
$716$	−10.1826			−0.380540
$717$	3.55582			0.132794
$718$		−	27.2394i		−	1.01656i
$719$	31.4990			1.17471			0.587357	−	0.809328i	$-0.300168\pi$
$719$	31.4990			1.17471			0.587357	+	0.809328i	$0.300168\pi$
$720$		0			0
$721$		−	51.4768i		−	1.91709i
$722$	−17.7779			−0.661625
$723$	−63.8703			−2.37536
$724$	11.3935			0.423437
$725$		0			0
$726$			26.8093i			0.994987i
$727$		−	22.8814i		−	0.848625i	−0.905516	−	0.424312i	$-0.860516\pi$
$727$		−	22.8814i		−	0.848625i	0.905516	−	0.424312i	$-0.139484\pi$
$728$	−13.8550	+	5.21097i	−0.513500	+	0.193131i
$729$	4.36710			0.161745
$730$		0			0
$731$	12.0000			0.443836
$732$			44.4595i			1.64327i
$733$	−48.1126			−1.77708			−0.888541	−	0.458798i	$-0.848280\pi$
$733$	−48.1126			−1.77708			−0.888541	+	0.458798i	$0.848280\pi$
$734$		−	23.8641i		−	0.880841i
$735$		0			0
$736$			6.74950i			0.248790i
$737$			5.76876i			0.212495i
$738$		−	52.1887i		−	1.92109i
$739$			19.9321i			0.733213i	0.930376	+	0.366606i	$0.119480\pi$
$739$			19.9321i			0.733213i	−0.930376	+	0.366606i	$0.880520\pi$
$740$		0			0
$741$	11.5857	−	4.35748i	0.425612	−	0.160076i
$742$			1.77791i			0.0652691i
$743$	24.6248			0.903395			0.451698	−	0.892171i	$-0.350819\pi$
$743$	24.6248			0.903395			0.451698	+	0.892171i	$0.350819\pi$
$744$	−26.8439			−0.984144
$745$		0			0
$746$			22.3164i			0.817063i
$747$	−29.6420			−1.08455
$748$	−4.61562			−0.168764
$749$			7.46146i			0.272636i
$750$		0			0
$751$	−36.7273			−1.34020			−0.670098	−	0.742272i	$-0.733748\pi$
$751$	−36.7273			−1.34020			−0.670098	+	0.742272i	$0.733748\pi$
$752$	−10.8550			−0.395841
$753$		−	10.2992i		−	0.375323i
$754$	−18.7871	+	7.06595i	−0.684184	+	0.257327i
$755$		0			0
$756$			46.4595i			1.68971i
$757$		−	37.0091i		−	1.34512i	−0.740042	−	0.672560i	$-0.765195\pi$
$757$		−	37.0091i		−	1.34512i	0.740042	−	0.672560i	$-0.234805\pi$
$758$		−	9.74950i		−	0.354118i
$759$			32.2485i			1.17055i
$760$		0			0
$761$		−	26.6420i		−	0.965773i	−0.875683	−	0.482887i	$-0.839588\pi$
$761$		−	26.6420i		−	0.965773i	0.875683	−	0.482887i	$-0.160412\pi$
$762$	15.2880			0.553827
$763$		−	15.0771i		−	0.545827i
$764$	−19.4990			−0.705449
$765$		0			0
$766$	−24.7871			−0.895593
$767$	17.4879	+	46.4970i	0.631451	+	1.67891i
$768$		−	3.10548i		−	0.112059i
$769$		−	37.2972i		−	1.34497i	−0.740110	−	0.672486i	$-0.765227\pi$
$769$		−	37.2972i		−	1.34497i	0.740110	−	0.672486i	$-0.234773\pi$
$770$		0			0
$771$	−38.6106			−1.39053
$772$	2.72110			0.0979346
$773$	−10.5385			−0.379045			−0.189522	−	0.981876i	$-0.560694\pi$
$773$	−10.5385			−0.379045			−0.189522	+	0.981876i	$0.560694\pi$
$774$			26.5761i			0.955258i
$775$		0			0
$776$	3.78903			0.136018
$777$			57.8641i			2.07586i
$778$	−0.749505			−0.0268711
$779$	8.68355			0.311121
$780$		0			0
$781$		0			0
$782$	20.2485			0.724085
$783$			62.9980i			2.25137i
$784$	9.85499			0.351964
$785$		0			0
$786$			2.68970i			0.0959385i
$787$	0.278898			0.00994165			0.00497083	−	0.999988i	$-0.498418\pi$
$787$	0.278898			0.00994165			0.00497083	+	0.999988i	$0.498418\pi$
$788$	1.61562			0.0575540
$789$	13.6156			0.484729
$790$		0			0
$791$			65.9585i			2.34521i
$792$		−	10.2221i		−	0.363226i
$793$	−48.3145	+	18.1714i	−1.71570	+	0.645287i
$794$	−9.67243			−0.343262
$795$		0			0
$796$	22.2485			0.788578
$797$			42.0832i			1.49066i	0.666693	+	0.745332i	$0.267709\pi$
$797$			42.0832i			1.49066i	−0.666693	+	0.745332i	$0.732291\pi$
$798$	−14.0944			−0.498935
$799$			32.5650i			1.15207i
$800$		0			0
$801$		−	12.3246i		−	0.435468i
$802$			10.9321i			0.386025i
$803$		−	16.5822i		−	0.585175i
$804$			11.6440i			0.410653i
$805$		0			0
$806$	−10.9716	−	29.1714i	−0.386458	−	1.02752i
$807$		−	17.2880i		−	0.608568i
$808$	−7.18256			−0.252682
$809$	12.6329			0.444149			0.222074	−	0.975030i	$-0.428717\pi$
$809$	12.6329			0.444149			0.222074	+	0.975030i	$0.428717\pi$
$810$		0			0
$811$		−	43.1411i		−	1.51489i	−0.652901	−	0.757444i	$-0.726448\pi$
$811$		−	43.1411i		−	1.51489i	0.652901	−	0.757444i	$-0.273552\pi$
$812$	22.8550			0.802053
$813$	29.1714			1.02309
$814$		−	6.98272i		−	0.244744i
$815$		0			0
$816$	−9.31645			−0.326141
$817$	−4.42193			−0.154704
$818$			26.5669i			0.928891i
$819$	−92.0528	+	34.6218i	−3.21659	+	1.20978i
$820$		0			0
$821$		−	23.0173i		−	0.803308i	−0.915791	−	0.401654i	$-0.868435\pi$
$821$		−	23.0173i		−	0.803308i	0.915791	−	0.401654i	$-0.131565\pi$
$822$			52.1035i			1.81732i
$823$			4.00000i			0.139431i	0.997567	+	0.0697156i	$0.0222092\pi$
$823$			4.00000i			0.139431i	−0.997567	+	0.0697156i	$0.977791\pi$
$824$			12.5385i			0.436801i
$825$		0			0
$826$		−	56.5650i		−	1.96815i
$827$	35.4027			1.23107			0.615536	−	0.788109i	$-0.288940\pi$
$827$	35.4027			1.23107			0.615536	+	0.788109i	$0.288940\pi$
$828$			44.8439i			1.55843i
$829$	10.6065			0.368378			0.184189	−	0.982891i	$-0.441034\pi$
$829$	10.6065			0.368378			0.184189	+	0.982891i	$0.441034\pi$
$830$		0			0
$831$	−26.0375			−0.903233
$832$	3.37475	−	1.26927i	0.116998	−	0.0440040i
$833$		−	29.5650i		−	1.02437i
$834$			13.6440i			0.472454i
$835$		0			0
$836$	1.70083			0.0588244
$837$	−97.8196			−3.38114
$838$	24.3145			0.839929
$839$		−	19.4615i		−	0.671884i	−0.941883	−	0.335942i	$-0.890945\pi$
$839$		−	19.4615i		−	0.671884i	0.941883	−	0.335942i	$-0.109055\pi$
$840$		0			0
$841$	1.99085			0.0686501
$842$		−	6.15416i		−	0.212086i
$843$	39.2312			1.35120
$844$	10.2394			0.352454
$845$		0			0
$846$	−72.1208			−2.47956
$847$	35.4422			1.21781
$848$		−	0.433057i		−	0.0148712i
$849$	−41.8327			−1.43570
$850$		0			0
$851$			30.6329i			1.05008i
$852$		0			0
$853$	15.9807			0.547170			0.273585	−	0.961848i	$-0.411790\pi$
$853$	15.9807			0.547170			0.273585	+	0.961848i	$0.411790\pi$
$854$	58.7759			2.01127
$855$		0			0
$856$		−	1.81744i		−	0.0621188i
$857$		−	38.5669i		−	1.31742i	−0.752396	−	0.658711i	$-0.771102\pi$
$857$		−	38.5669i		−	1.31742i	0.752396	−	0.658711i	$-0.228898\pi$
$858$	16.1243	−	6.06445i	0.550473	−	0.207037i
$859$	28.6836			0.978670			0.489335	−	0.872096i	$-0.337240\pi$
$859$	28.6836			0.978670			0.489335	+	0.872096i	$0.337240\pi$
$860$		0			0
$861$	−100.147			−3.41301
$862$			0.828565i			0.0282210i
$863$	−36.4706			−1.24147			−0.620737	−	0.784019i	$-0.713166\pi$
$863$	−36.4706			−1.24147			−0.620737	+	0.784019i	$0.713166\pi$
$864$		−	11.3164i		−	0.384993i
$865$		0			0
$866$		−	15.7008i		−	0.533536i
$867$		−	24.8439i		−	0.843742i
$868$			35.4879i			1.20454i
$869$		−	10.0598i		−	0.341255i
$870$		0			0
$871$	−12.6537	+	4.75913i	−0.428753	+	0.161257i
$872$			3.67243i			0.124364i
$873$	25.1744			0.852025
$874$	−7.46146			−0.252388
$875$		0			0
$876$		−	33.4706i		−	1.13087i
$877$	7.02027			0.237058			0.118529	−	0.992951i	$-0.462182\pi$
$877$	7.02027			0.237058			0.118529	+	0.992951i	$0.462182\pi$
$878$	−9.17144			−0.309521
$879$		−	18.6329i		−	0.628472i
$880$		0			0
$881$	4.93405			0.166232			0.0831161	−	0.996540i	$-0.473513\pi$
$881$	4.93405			0.166232			0.0831161	+	0.996540i	$0.473513\pi$
$882$	65.4768			2.20472
$883$		−	49.9493i		−	1.68093i	−0.541866	−	0.840465i	$-0.682282\pi$
$883$		−	49.9493i		−	1.68093i	0.541866	−	0.840465i	$-0.317718\pi$
$884$	−3.80781	−	10.1243i	−0.128070	−	0.340516i
$885$		0			0
$886$		−	15.3164i		−	0.514566i
$887$			3.86413i			0.129745i	0.997894	+	0.0648725i	$0.0206641\pi$
$887$			3.86413i			0.129745i	−0.997894	+	0.0648725i	$0.979336\pi$
$888$		−	14.0944i		−	0.472976i
$889$		−	20.2110i		−	0.677854i
$890$		0			0
$891$		−	23.4027i		−	0.784019i
$892$	20.9605			0.701808
$893$		−	12.0000i		−	0.401565i
$894$	−30.1542			−1.00851
$895$		0			0
$896$	−4.10548			−0.137155
$897$	−70.7364	+	26.6045i	−2.36182	+	0.888298i
$898$			23.4108i			0.781229i
$899$			48.1208i			1.60492i
$900$		0			0
$901$	−1.29917			−0.0432817
$902$	12.0852			0.402393
$903$	50.9980			1.69711
$904$		−	16.0660i		−	0.534346i
$905$		0			0
$906$	7.73223			0.256886
$907$		−	17.5558i		−	0.582931i	−0.956581	−	0.291466i	$-0.905857\pi$
$907$		−	17.5558i		−	0.582931i	0.956581	−	0.291466i	$-0.0941429\pi$
$908$	4.85499			0.161118
$909$	−47.7211			−1.58281
$910$		0			0
$911$	−27.9807			−0.927043			−0.463522	−	0.886086i	$-0.653414\pi$
$911$	−27.9807			−0.927043			−0.463522	+	0.886086i	$0.653414\pi$
$912$	3.43306			0.113680
$913$		−	6.86413i		−	0.227170i
$914$	−22.9321			−0.758525
$915$		0			0
$916$			6.71196i			0.221769i
$917$	3.55582			0.117423
$918$	−33.9493			−1.12050
$919$	−31.0356			−1.02377			−0.511884	−	0.859054i	$-0.671052\pi$
$919$	−31.0356			−1.02377			−0.511884	+	0.859054i	$0.671052\pi$
$920$		0			0
$921$			43.1430i			1.42161i
$922$		−	13.4615i		−	0.443330i
$923$		0			0
$924$	−19.6156			−0.645306
$925$		0			0
$926$	16.0264			0.526661
$927$			83.3063i			2.73614i
$928$	−5.56694			−0.182744
$929$			24.0000i			0.787414i	0.919236	+	0.393707i	$0.128808\pi$
$929$			24.0000i			0.787414i	−0.919236	+	0.393707i	$0.871192\pi$
$930$		0			0
$931$			10.8945i			0.357053i
$932$			14.3651i			0.470545i
$933$		−	10.9259i		−	0.357698i
$934$		−	0.866114i		−	0.0283401i
$935$		0			0
$936$	22.4219	−	8.43306i	0.732884	−	0.275643i
$937$		−	60.8987i		−	1.98947i	−0.102464	−	0.994737i	$-0.532673\pi$
$937$		−	60.8987i		−	1.98947i	0.102464	−	0.994737i	$-0.467327\pi$
$938$	15.3935			0.502616
$939$	−76.2861			−2.48950
$940$		0			0
$941$		−	32.2485i		−	1.05127i	−0.850710	−	0.525636i	$-0.823827\pi$
$941$		−	32.2485i		−	1.05127i	0.850710	−	0.525636i	$-0.176173\pi$
$942$	−35.3824			−1.15282
$943$	−53.0173			−1.72648
$944$			13.7779i			0.448433i
$945$		0			0
$946$	−6.15416			−0.200089
$947$	−20.4108			−0.663262			−0.331631	−	0.943409i	$-0.607599\pi$
$947$	−20.4108			−0.663262			−0.331631	+	0.943409i	$0.607599\pi$
$948$		−	20.3053i		−	0.659486i
$949$	36.3728	−	13.6801i	1.18071	−	0.444074i
$950$		0			0
$951$			4.53854i			0.147172i
$952$			12.3164i			0.399178i
$953$		−	8.36710i		−	0.271037i	−0.990775	−	0.135519i	$-0.956730\pi$
$953$		−	8.36710i		−	0.271037i	0.990775	−	0.135519i	$-0.0432700\pi$
$954$		−	2.87724i		−	0.0931541i
$955$		0			0
$956$			1.14501i			0.0370324i
$957$	−26.5983			−0.859802
$958$		−	29.4879i		−	0.952710i
$959$	68.8814			2.22430
$960$		0			0
$961$	−43.7191			−1.41029
$962$	15.3164	−	5.76063i	0.493822	−	0.185730i
$963$		−	12.0751i		−	0.389115i
$964$		−	20.5669i		−	0.662417i
$965$		0			0
$966$	86.0528			2.76870
$967$	14.4108			0.463420			0.231710	−	0.972785i	$-0.425568\pi$
$967$	14.4108			0.463420			0.231710	+	0.972785i	$0.425568\pi$
$968$	−8.63290			−0.277472
$969$		−	10.2992i		−	0.330857i
$970$		0			0
$971$	25.1806			0.808083			0.404042	−	0.914741i	$-0.367605\pi$
$971$	25.1806			0.808083			0.404042	+	0.914741i	$0.367605\pi$
$972$		−	13.2880i		−	0.426214i
$973$	18.0375			0.578257
$974$	35.4503			1.13590
$975$		0			0
$976$	−14.3164			−0.458258
$977$	−38.1633			−1.22095			−0.610476	−	0.792035i	$-0.709022\pi$
$977$	−38.1633			−1.22095			−0.610476	+	0.792035i	$0.709022\pi$
$978$		−	52.2201i		−	1.66982i
$979$	2.85397			0.0912133
$980$		0			0
$981$			24.3997i			0.779022i
$982$	32.1319			1.02537
$983$	49.8906			1.59126			0.795631	−	0.605782i	$-0.207140\pi$
$983$	49.8906			1.59126			0.795631	+	0.605782i	$0.207140\pi$
$984$	24.3935			0.777637
$985$		0			0
$986$			16.7008i			0.531863i
$987$			138.396i			4.40518i
$988$	1.40316	+	3.73073i	0.0446403	+	0.118690i
$989$	26.9980			0.858487
$990$		0			0
$991$	−10.6329			−0.337765			−0.168883	−	0.985636i	$-0.554016\pi$
$991$	−10.6329			−0.337765			−0.168883	+	0.985636i	$0.554016\pi$
$992$		−	8.64402i		−	0.274448i
$993$	56.6420			1.79748
$994$		0			0
$995$		0			0
$996$		−	13.8550i		−	0.439012i
$997$			2.99085i			0.0947213i	0.998878	+	0.0473606i	$0.0150810\pi$
$997$			2.99085i			0.0947213i	−0.998878	+	0.0473606i	$0.984919\pi$
$998$			27.2769i			0.863436i
$999$		−	51.3601i		−	1.62496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.c.e.649.1		6
5.2	odd	4		650.2.d.c.51.1	✓	6
5.3	odd	4		650.2.d.d.51.6	yes	6
5.4	even	2		650.2.c.f.649.6		6
13.12	even	2		650.2.c.f.649.1		6
65.8	even	4		8450.2.a.bq.1.3		3
65.12	odd	4		650.2.d.c.51.4	yes	6
65.18	even	4		8450.2.a.ce.1.3		3
65.38	odd	4		650.2.d.d.51.3	yes	6
65.47	even	4		8450.2.a.cd.1.1		3
65.57	even	4		8450.2.a.br.1.1		3
65.64	even	2	inner	650.2.c.e.649.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.c.e.649.1		6	1.1	even	1	trivial
650.2.c.e.649.6		6	65.64	even	2	inner
650.2.c.f.649.1		6	13.12	even	2
650.2.c.f.649.6		6	5.4	even	2
650.2.d.c.51.1	✓	6	5.2	odd	4
650.2.d.c.51.4	yes	6	65.12	odd	4
650.2.d.d.51.3	yes	6	65.38	odd	4
650.2.d.d.51.6	yes	6	5.3	odd	4
8450.2.a.bq.1.3		3	65.8	even	4
8450.2.a.br.1.1		3	65.57	even	4
8450.2.a.cd.1.1		3	65.47	even	4
8450.2.a.ce.1.3		3	65.18	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.10548i q^{3} +1.00000 q^{4} +3.10548i q^{6} +4.10548 q^{7} -1.00000 q^{8} -6.64402 q^{9} -1.53854i q^{11} -3.10548i q^{12} +(3.37475 - 1.26927i) q^{13} -4.10548 q^{14} +1.00000 q^{16} -3.00000i q^{17} +6.64402 q^{18} +1.10548i q^{19} -12.7495i q^{21} +1.53854i q^{22} -6.74950i q^{23} +3.10548i q^{24} +(-3.37475 + 1.26927i) q^{26} +11.3164i q^{27} +4.10548 q^{28} +5.56694 q^{29} +8.64402i q^{31} -1.00000 q^{32} -4.77791 q^{33} +3.00000i q^{34} -6.64402 q^{36} -4.53854 q^{37} -1.10548i q^{38} +(-3.94170 - 10.4802i) q^{39} -7.85499i q^{41} +12.7495i q^{42} +4.00000i q^{43} -1.53854i q^{44} +6.74950i q^{46} -10.8550 q^{47} -3.10548i q^{48} +9.85499 q^{49} -9.31645 q^{51} +(3.37475 - 1.26927i) q^{52} -0.433057i q^{53} -11.3164i q^{54} -4.10548 q^{56} +3.43306 q^{57} -5.56694 q^{58} +13.7779i q^{59} -14.3164 q^{61} -8.64402i q^{62} -27.2769 q^{63} +1.00000 q^{64} +4.77791 q^{66} -3.74950 q^{67} -3.00000i q^{68} -20.9605 q^{69} +6.64402 q^{72} +10.7779 q^{73} +4.53854 q^{74} +1.10548i q^{76} -6.31645i q^{77} +(3.94170 + 10.4802i) q^{78} +6.53854 q^{79} +15.2110 q^{81} +7.85499i q^{82} +4.46146 q^{83} -12.7495i q^{84} -4.00000i q^{86} -17.2880i q^{87} +1.53854i q^{88} +1.85499i q^{89} +(13.8550 - 5.21097i) q^{91} -6.74950i q^{92} +26.8439 q^{93} +10.8550 q^{94} +3.10548i q^{96} -3.78903 q^{97} -9.85499 q^{98} +10.2221i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} + 6 q^{7} - 6 q^{8} - 18 q^{9} - 6 q^{14} + 6 q^{16} + 18 q^{18} + 6 q^{28} + 18 q^{29} - 6 q^{32} + 24 q^{33} - 18 q^{36} - 24 q^{37} + 12 q^{39} - 6 q^{47} - 6 q^{56} + 36 q^{57}+ \cdots - 60 q^{97}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 + 6 * q^7 - 6 * q^8 - 18 * q^9 - 6 * q^14 + 6 * q^16 + 18 * q^18 + 6 * q^28 + 18 * q^29 - 6 * q^32 + 24 * q^33 - 18 * q^36 - 24 * q^37 + 12 * q^39 - 6 * q^47 - 6 * q^56 + 36 * q^57 - 18 * q^58 - 30 * q^61 - 30 * q^63 + 6 * q^64 - 24 * q^66 + 18 * q^67 - 48 * q^69 + 18 * q^72 + 12 * q^73 + 24 * q^74 - 12 * q^78 + 36 * q^79 + 54 * q^81 + 30 * q^83 + 24 * q^91 + 12 * q^93 + 6 * q^94 - 60 * q^97

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